MinT - Best Known (154−73, 154, s)-Nets in Base 4

Best Known (154−73, 154, s)-Nets in Base 4

(154−73, 154, 104)-Net over F₄ — Constructive and digital

Digital (81, 154, 104)-net over F₄, using

t-expansion [i] based on digital (73, 154, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(154−73, 154, 136)-Net over F₄ — Digital

Digital (81, 154, 136)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(154−73, 154, 1694)-Net in Base 4 — Upper bound on s

There is no (81, 154, 1695)-net in base 4, because

1 times m-reduction [i] would yield (81, 153, 1695)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 133 034733 066131 899638 989723 323215 618065 516233 103756 256789 900464 127508 620623 356915 545192 158980 > 4¹⁵³ [i]