MinT - Best Known (148−53, 148, s)-Nets in Base 2

Best Known (148−53, 148, s)-Nets in Base 2

(148−53, 148, 68)-Net over F₂ — Constructive and digital

Digital (95, 148, 68)-net over F₂, using

trace code for nets [i] based on digital (21, 74, 34)-net over F₄, using
- net from sequence [i] based on digital (21, 33)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
    - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(148−53, 148, 93)-Net over F₂ — Digital

Digital (95, 148, 93)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−53, 148, 493)-Net in Base 2 — Upper bound on s

There is no (95, 148, 494)-net in base 2, because

1 times m-reduction [i] would yield (95, 147, 494)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 178 932295 457288 342253 005804 295806 420192 786420 > 2¹⁴⁷ [i]