MinT - Best Known (40−34, 40, s)-Nets in Base 256

Best Known (40−34, 40, s)-Nets in Base 256

(40−34, 40, 263)-Net over F₂₅₆ — Constructive and digital

Digital (6, 40, 263)-net over F₂₅₆, using

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

(40−34, 40, 321)-Net over F₂₅₆ — Digital

Digital (6, 40, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 40, 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]

(40−34, 40, 13049)-Net in Base 256 — Upper bound on s

There is no (6, 40, 13050)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 2 138232 839820 935192 131439 412657 774742 680067 563921 803955 491545 465623 166316 406858 661355 805360 569251 > 256⁴⁰ [i]