MinT - Best Known (72, 72+29, s)-Nets in Base 4

Best Known (72, 72+29, s)-Nets in Base 4

(72, 72+29, 312)-Net over F₄ — Constructive and digital

Digital (72, 101, 312)-net over F₄, using

t-expansion [i] based on digital (71, 101, 312)-net over F₄, using
- 1 times m-reduction [i] based on digital (71, 102, 312)-net over F₄, using
  - trace code for nets [i] based on digital (3, 34, 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]

(72, 72+29, 573)-Net over F₄ — Digital

Digital (72, 101, 573)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+29, 40238)-Net in Base 4 — Upper bound on s

There is no (72, 101, 40239)-net in base 4, because

1 times m-reduction [i] would yield (72, 100, 40239)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 607076 661042 384759 389902 719946 274477 570326 238549 614146 754557 > 4¹⁰⁰ [i]