MinT - Best Known (112, 199, s)-Nets in Base 4

Best Known (112, 199, s)-Nets in Base 4

(112, 199, 130)-Net over F₄ — Constructive and digital

Digital (112, 199, 130)-net over F₄, using

t-expansion [i] based on digital (105, 199, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(112, 199, 219)-Net over F₄ — Digital

Digital (112, 199, 219)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 199, 3296)-Net in Base 4 — Upper bound on s

There is no (112, 199, 3297)-net in base 4, because

1 times m-reduction [i] would yield (112, 198, 3297)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 163098 579650 006798 021722 396079 782577 083828 777119 566584 024817 863697 663712 774710 118650 724637 513221 883774 847867 351582 458816 > 4¹⁹⁸ [i]