MinT - Best Known (67−61, 67, s)-Nets in Base 256

Best Known (67−61, 67, s)-Nets in Base 256

(67−61, 67, 263)-Net over F₂₅₆ — Constructive and digital

Digital (6, 67, 263)-net over F₂₅₆, using

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

(67−61, 67, 321)-Net over F₂₅₆ — Digital

Digital (6, 67, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 67, 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]

(67−61, 67, 9369)-Net in Base 256 — Upper bound on s

There is no (6, 67, 9370)-net in base 256, because

1 times m-reduction [i] would yield (6, 66, 9370)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 881 124009 970180 757481 613988 597871 633226 965490 992358 871701 553869 792368 757257 853217 295138 608730 872754 687454 248253 181916 568998 848517 745670 794026 042963 255687 117376 > 256⁶⁶ [i]