MinT - Best Known (4, 4+42, s)-Nets in Base 256

Best Known (4, 4+42, s)-Nets in Base 256

(4, 4+42, 261)-Net over F₂₅₆ — Constructive and digital

Digital (4, 46, 261)-net over F₂₅₆, using

net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(4, 4+42, 321)-Net over F₂₅₆ — Digital

Digital (4, 46, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 46, 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]

(4, 4+42, 6404)-Net in Base 256 — Upper bound on s

There is no (4, 46, 6405)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 602 896255 586329 546624 950823 004667 240433 999028 064265 055183 838791 531907 363668 646757 790701 431564 374977 485139 883776 > 256⁴⁶ [i]