MinT - Best Known (237−69, 237, s)-Nets in Base 2

Best Known (237−69, 237, s)-Nets in Base 2

(237−69, 237, 138)-Net over F₂ — Constructive and digital

Digital (168, 237, 138)-net over F₂, using

trace code for nets [i] based on digital (10, 79, 46)-net over F₈, using
- net from sequence [i] based on digital (10, 45)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₈ with g(F)Â =Â 9, N(F)Â =Â 45, and 1 place with degree 2 [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]

(237−69, 237, 222)-Net over F₂ — Digital

Digital (168, 237, 222)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−69, 237, 1613)-Net in Base 2 — Upper bound on s

There is no (168, 237, 1614)-net in base 2, because

1 times m-reduction [i] would yield (168, 236, 1614)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 111520 840476 795378 717949 439003 219536 747898 671398 548721 496789 426617 269428 > 2²³⁶ [i]