MinT - Best Known (72, 72+31, s)-Nets in Base 4

Best Known (72, 72+31, s)-Nets in Base 4

(72, 72+31, 312)-Net over F₄ — Constructive and digital

Digital (72, 103, 312)-net over F₄, using

4¹ times duplication [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+31, 483)-Net over F₄ — Digital

Digital (72, 103, 483)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+31, 26574)-Net in Base 4 — Upper bound on s

There is no (72, 103, 26575)-net in base 4, because

1 times m-reduction [i] would yield (72, 102, 26575)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 25 725198 064605 073671 779787 798362 127902 999845 562274 233487 403036 > 4¹⁰² [i]