MinT - Best Known (61−55, 61, s)-Nets in Base 256

Best Known (61−55, 61, s)-Nets in Base 256

(61−55, 61, 263)-Net over F₂₅₆ — Constructive and digital

Digital (6, 61, 263)-net over F₂₅₆, using

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

(61−55, 61, 321)-Net over F₂₅₆ — Digital

Digital (6, 61, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 61, 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]

(61−55, 61, 9614)-Net in Base 256 — Upper bound on s

There is no (6, 61, 9615)-net in base 256, because

1 times m-reduction [i] would yield (6, 60, 9615)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 3 127528 139946 194681 686389 923237 152671 012522 615294 237232 629325 162786 896644 616742 215914 191138 332224 522308 929990 671257 028405 011202 237776 928631 959776 > 256⁶⁰ [i]