MinT - Best Known (32, 32+30, s)-Nets in Base 7

Best Known (32, 32+30, s)-Nets in Base 7

(32, 32+30, 102)-Net over F₇ — Constructive and digital

Digital (32, 62, 102)-net over F₇, using

trace code for nets [i] based on digital (1, 31, 51)-net over F₄₉, using
- net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(32, 32+30, 128)-Net over F₇ — Digital

Digital (32, 62, 128)-net over F₇, using

trace code for nets [i] based on digital (1, 31, 64)-net over F₄₉, using
- net from sequence [i] based on digital (1, 63)-sequence over F₄₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 1 and N(F) ≥ 64, using
    - sharp bound on the number of rational points on curves with genus 1 [i]

(32, 32+30, 3322)-Net in Base 7 — Upper bound on s

There is no (32, 62, 3323)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 24963 420106 784768 202024 920425 876233 242248 041406 845511 > 7⁶² [i]