MinT - Best Known (112, 112+141, s)-Nets in Base 2

Best Known (112, 112+141, s)-Nets in Base 2

(112, 112+141, 57)-Net over F₂ — Constructive and digital

Digital (112, 253, 57)-net over F₂, using

t-expansion [i] based on digital (110, 253, 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]

(112, 112+141, 72)-Net over F₂ — Digital

Digital (112, 253, 72)-net over F₂, using

t-expansion [i] based on digital (110, 253, 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]

(112, 112+141, 234)-Net in Base 2 — Upper bound on s

There is no (112, 253, 235)-net in base 2, because

1 times m-reduction [i] would yield (112, 252, 235)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7691 245391 386056 349166 901571 610679 242434 100382 694756 830719 846385 376048 032818 > 2²⁵² [i]