MinT - Best Known (132, 132+89, s)-Nets in Base 2

Best Known (132, 132+89, s)-Nets in Base 2

(132, 132+89, 68)-Net over F₂ — Constructive and digital

Digital (132, 221, 68)-net over F₂, using

1 times m-reduction [i] based on digital (132, 222, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 111, 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]

(132, 132+89, 99)-Net over F₂ — Digital

Digital (132, 221, 99)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(132, 132+89, 490)-Net in Base 2 — Upper bound on s

There is no (132, 221, 491)-net in base 2, because

1 times m-reduction [i] would yield (132, 220, 491)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 824066 441442 010372 228916 119896 679993 579793 178492 567871 846986 004248 > 2²²⁰ [i]