MinT - Best Known (260−81, 260, s)-Nets in Base 2

Best Known (260−81, 260, s)-Nets in Base 2

(260−81, 260, 132)-Net over F₂ — Constructive and digital

Digital (179, 260, 132)-net over F₂, using

trace code for nets [i] based on digital (49, 130, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(260−81, 260, 204)-Net over F₂ — Digital

Digital (179, 260, 204)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(260−81, 260, 1344)-Net in Base 2 — Upper bound on s

There is no (179, 260, 1345)-net in base 2, because

1 times m-reduction [i] would yield (179, 259, 1345)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 944581 853510 599666 261836 025436 025270 464450 836109 186384 718748 683290 921723 899560 > 2²⁵⁹ [i]