MinT - Best Known (108, 108+149, s)-Nets in Base 2

Best Known (108, 108+149, s)-Nets in Base 2

(108, 108+149, 56)-Net over F₂ — Constructive and digital

Digital (108, 257, 56)-net over F₂, using

t-expansion [i] based on digital (105, 257, 56)-net over F₂, using
- net from sequence [i] based on digital (105, 55)-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 7 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]

(108, 108+149, 65)-Net over F₂ — Digital

Digital (108, 257, 65)-net over F₂, using

t-expansion [i] based on digital (95, 257, 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]

(108, 108+149, 216)-Net in Base 2 — Upper bound on s

There is no (108, 257, 217)-net in base 2, because

1 times m-reduction [i] would yield (108, 256, 217)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 123827 639781 033565 867357 364581 192635 899659 105010 500409 504469 504987 414369 553564 > 2²⁵⁶ [i]