MinT - Best Known (84, 84+37, s)-Nets in Base 4

Best Known (84, 84+37, s)-Nets in Base 4

(84, 84+37, 312)-Net over F₄ — Constructive and digital

Digital (84, 121, 312)-net over F₄, using

4¹ times duplication [i] based on digital (83, 120, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 40, 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]

(84, 84+37, 513)-Net over F₄ — Digital

Digital (84, 121, 513)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+37, 25971)-Net in Base 4 — Upper bound on s

There is no (84, 121, 25972)-net in base 4, because

1 times m-reduction [i] would yield (84, 120, 25972)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 767261 629749 161044 490782 938381 842740 166845 792319 068907 707537 907373 699153 > 4¹²⁰ [i]