MinT - Best Known (237−67, 237, s)-Nets in Base 4

Best Known (237−67, 237, s)-Nets in Base 4

(237−67, 237, 531)-Net over F₄ — Constructive and digital

Digital (170, 237, 531)-net over F₄, using

t-expansion [i] based on digital (169, 237, 531)-net over F₄, using
- 6 times m-reduction [i] based on digital (169, 243, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 81, 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]

(237−67, 237, 1234)-Net over F₄ — Digital

Digital (170, 237, 1234)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−67, 237, 88662)-Net in Base 4 — Upper bound on s

There is no (170, 237, 88663)-net in base 4, because

1 times m-reduction [i] would yield (170, 236, 88663)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12194 916200 722513 788298 624532 225358 254893 148553 514002 584768 591017 753817 034260 581522 499813 118937 444521 782353 468691 870014 629647 687386 345545 423340 > 4²³⁶ [i]