MinT - Best Known (98−25, 98, s)-Nets in Base 2

Best Known (98−25, 98, s)-Nets in Base 2

(98−25, 98, 102)-Net over F₂ — Constructive and digital

Digital (73, 98, 102)-net over F₂, using

1 times m-reduction [i] based on digital (73, 99, 102)-net over F₂, using
- trace code for nets [i] based on digital (7, 33, 34)-net over F₈, using
  - net from sequence [i] based on digital (7, 33)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]

(98−25, 98, 151)-Net over F₂ — Digital

Digital (73, 98, 151)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(98−25, 98, 1417)-Net in Base 2 — Upper bound on s

There is no (73, 98, 1418)-net in base 2, because

1 times m-reduction [i] would yield (73, 97, 1418)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 159718 329446 904229 842479 622192 > 2⁹⁷ [i]