MinT - Best Known (63−57, 63, s)-Nets in Base 256

Best Known (63−57, 63, s)-Nets in Base 256

(63−57, 63, 263)-Net over F₂₅₆ — Constructive and digital

Digital (6, 63, 263)-net over F₂₅₆, using

net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(63−57, 63, 321)-Net over F₂₅₆ — Digital

Digital (6, 63, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 63, 321)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 320)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
    - sharp bound on the number of rational points on curves with genus 2 [i]

(63−57, 63, 9514)-Net in Base 256 — Upper bound on s

There is no (6, 63, 9515)-net in base 256, because

1 times m-reduction [i] would yield (6, 62, 9515)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 205025 020741 904617 004931 974662 687520 453225 389427 229650 474571 007793 055413 971094 847258 905932 978690 487008 948067 342256 874869 249108 132158 973390 487051 677976 > 256⁶² [i]