MinT - Best Known (167−47, 167, s)-Nets in Base 4

Best Known (167−47, 167, s)-Nets in Base 4

(167−47, 167, 531)-Net over F₄ — Constructive and digital

Digital (120, 167, 531)-net over F₄, using

t-expansion [i] based on digital (119, 167, 531)-net over F₄, using
- 1 times m-reduction [i] based on digital (119, 168, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 56, 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]

(167−47, 167, 943)-Net over F₄ — Digital

Digital (120, 167, 943)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(167−47, 167, 69585)-Net in Base 4 — Upper bound on s

There is no (120, 167, 69586)-net in base 4, because

1 times m-reduction [i] would yield (120, 166, 69586)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8749 362025 501148 241651 249690 940167 735934 235297 907690 627919 875958 115448 330927 995395 123648 005221 598304 > 4¹⁶⁶ [i]