MinT - Best Known (113, 113+141, s)-Nets in Base 2

Best Known (113, 113+141, s)-Nets in Base 2

(113, 113+141, 57)-Net over F₂ — Constructive and digital

Digital (113, 254, 57)-net over F₂, using

t-expansion [i] based on digital (110, 254, 57)-net over F₂, using
- net from sequence [i] based on digital (110, 56)-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 8 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]

(113, 113+141, 72)-Net over F₂ — Digital

Digital (113, 254, 72)-net over F₂, using

t-expansion [i] based on digital (110, 254, 72)-net over F₂, using
- net from sequence [i] based on digital (110, 71)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 110 and N(F) ≥ 72, using
    - Drinfeld modules of rank 1 [i]

(113, 113+141, 237)-Net in Base 2 — Upper bound on s

There is no (113, 254, 238)-net in base 2, because

1 times m-reduction [i] would yield (113, 253, 238)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14925 746718 025137 938078 734004 584717 759054 249926 505087 939010 588316 036527 787244 > 2²⁵³ [i]