MinT - Best Known (4, 4+39, s)-Nets in Base 256

Best Known (4, 4+39, s)-Nets in Base 256

(4, 4+39, 261)-Net over F₂₅₆ — Constructive and digital

Digital (4, 43, 261)-net over F₂₅₆, using

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

(4, 4+39, 321)-Net over F₂₅₆ — Digital

Digital (4, 43, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 43, 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+39, 6539)-Net in Base 256 — Upper bound on s

There is no (4, 43, 6540)-net in base 256, because

1 times m-reduction [i] would yield (4, 42, 6540)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 140147 220880 233803 175729 073336 724953 761346 096622 836058 479465 076094 247178 577310 298175 991318 940539 091176 > 256⁴² [i]