MinT - Best Known (96, 96+79, s)-Nets in Base 2

Best Known (96, 96+79, s)-Nets in Base 2

(96, 96+79, 54)-Net over F₂ — Constructive and digital

Digital (96, 175, 54)-net over F₂, using

t-expansion [i] based on digital (95, 175, 54)-net over F₂, using
- net from sequence [i] based on digital (95, 53)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 69, N(F)Â =Â 48, 1 place with degree 2, and 5 places with degree 6 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]

(96, 96+79, 65)-Net over F₂ — Digital

Digital (96, 175, 65)-net over F₂, using

t-expansion [i] based on digital (95, 175, 65)-net over F₂, using
- net from sequence [i] based on digital (95, 64)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 95 and N(F) ≥ 65, using
    - Drinfeld modules of rank 1 [i]

(96, 96+79, 285)-Net in Base 2 — Upper bound on s

There is no (96, 175, 286)-net in base 2, because

1 times m-reduction [i] would yield (96, 174, 286)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 25767 481140 254361 886260 220267 475849 107269 748266 237504 > 2¹⁷⁴ [i]