MinT - Best Known (13, 30, s)-Nets in Base 32

Best Known (13, 30, s)-Nets in Base 32

(13, 30, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 30, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 30, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(13, 30, 154)-Net over F₃₂ — Digital

Digital (13, 30, 154)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(13, 30, 258)-Net in Base 32 — Constructive

(13, 30, 258)-net in base 32, using

2 times m-reduction [i] based on (13, 32, 258)-net in base 32, using
- base change [i] based on digital (1, 20, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(13, 30, 289)-Net in Base 32

(13, 30, 289)-net in base 32, using

2 times m-reduction [i] based on (13, 32, 289)-net in base 32, using
- base change [i] based on digital (1, 20, 289)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 288)-sequence over F₂₅₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
      - sharp bound on the number of rational points on curves with genus 1 [i]

(13, 30, 34709)-Net in Base 32 — Upper bound on s

There is no (13, 30, 34710)-net in base 32, because

1 times m-reduction [i] would yield (13, 29, 34710)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 44 605260 062101 345944 959411 719155 940257 192338 > 32²⁹ [i]