MinT - Best Known (260−145, 260, s)-Nets in Base 2

Best Known (260−145, 260, s)-Nets in Base 2

(260−145, 260, 57)-Net over F₂ — Constructive and digital

Digital (115, 260, 57)-net over F₂, using

t-expansion [i] based on digital (110, 260, 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]

(260−145, 260, 73)-Net over F₂ — Digital

Digital (115, 260, 73)-net over F₂, using

t-expansion [i] based on digital (114, 260, 73)-net over F₂, using
- net from sequence [i] based on digital (114, 72)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 114 and N(F) ≥ 73, using
    - Drinfeld modules of rank 1 [i]

(260−145, 260, 240)-Net in Base 2 — Upper bound on s

There is no (115, 260, 241)-net in base 2, because

1 times m-reduction [i] would yield (115, 259, 241)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 042033 625807 932390 661843 842222 609705 453180 861419 658819 583593 022369 637050 799418 > 2²⁵⁹ [i]