MinT - Best Known (42−35, 42, s)-Nets in Base 256

Best Known (42−35, 42, s)-Nets in Base 256

(42−35, 42, 264)-Net over F₂₅₆ — Constructive and digital

Digital (7, 42, 264)-net over F₂₅₆, using

net from sequence [i] based on digital (7, 263)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(42−35, 42, 321)-Net over F₂₅₆ — Digital

Digital (7, 42, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 42, 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]

(42−35, 42, 18085)-Net in Base 256 — Upper bound on s

There is no (7, 42, 18086)-net in base 256, because

1 times m-reduction [i] would yield (7, 41, 18086)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 547 305022 480015 565597 355013 038781 355451 864538 708979 914267 237186 894109 662839 362710 056537 632399 031586 > 256⁴¹ [i]