MinT - Best Known (151, 151+77, s)-Nets in Base 2

Best Known (151, 151+77, s)-Nets in Base 2

(151, 151+77, 112)-Net over F₂ — Constructive and digital

Digital (151, 228, 112)-net over F₂, using

8 times m-reduction [i] based on digital (151, 236, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 118, 56)-net over F₄, using
  - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
      - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(151, 151+77, 152)-Net over F₂ — Digital

Digital (151, 228, 152)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(151, 151+77, 889)-Net in Base 2 — Upper bound on s

There is no (151, 228, 890)-net in base 2, because

1 times m-reduction [i] would yield (151, 227, 890)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 222 804043 946137 599806 324115 375559 756541 111103 761182 947284 953773 741836 > 2²²⁷ [i]