MinT - Best Known (148−47, 148, s)-Nets in Base 4

Best Known (148−47, 148, s)-Nets in Base 4

(148−47, 148, 240)-Net over F₄ — Constructive and digital

Digital (101, 148, 240)-net over F₄, using

2 times m-reduction [i] based on digital (101, 150, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 50, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(148−47, 148, 514)-Net over F₄ — Digital

Digital (101, 148, 514)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−47, 148, 22126)-Net in Base 4 — Upper bound on s

There is no (101, 148, 22127)-net in base 4, because

1 times m-reduction [i] would yield (101, 147, 22127)-net in base 4, but
- 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]