MinT - Best Known (71, 71+29, s)-Nets in Base 4

Best Known (71, 71+29, s)-Nets in Base 4

(71, 71+29, 312)-Net over F₄ — Constructive and digital

Digital (71, 100, 312)-net over F₄, using

2 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]

(71, 71+29, 546)-Net over F₄ — Digital

Digital (71, 100, 546)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+29, 36444)-Net in Base 4 — Upper bound on s

There is no (71, 100, 36445)-net in base 4, because

1 times m-reduction [i] would yield (71, 99, 36445)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 401867 612231 111090 945160 896680 662763 115420 238876 074941 784680 > 4⁹⁹ [i]