MinT - Best Known (178−51, 178, s)-Nets in Base 4

Best Known (178−51, 178, s)-Nets in Base 4

(178−51, 178, 531)-Net over F₄ — Constructive and digital

Digital (127, 178, 531)-net over F₄, using

2 times m-reduction [i] based on digital (127, 180, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 60, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(178−51, 178, 917)-Net over F₄ — Digital

Digital (127, 178, 917)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−51, 178, 62079)-Net in Base 4 — Upper bound on s

There is no (127, 178, 62080)-net in base 4, because

1 times m-reduction [i] would yield (127, 177, 62080)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 36705 701105 358071 966053 811449 559859 715289 959983 422979 969947 328221 129205 699662 836858 242295 220147 499955 903993 > 4¹⁷⁷ [i]