MinT - Best Known (147−46, 147, s)-Nets in Base 4

Best Known (147−46, 147, s)-Nets in Base 4

(147−46, 147, 312)-Net over F₄ — Constructive and digital

Digital (101, 147, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 49, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(147−46, 147, 542)-Net over F₄ — Digital

Digital (101, 147, 542)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−46, 147, 22126)-Net in Base 4 — Upper bound on s

There is no (101, 147, 22127)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31837 073710 748150 339237 538187 696923 652804 272584 985154 063358 803798 645683 618072 832565 773768 > 4¹⁴⁷ [i]