MinT - Best Known (79, 79+167, s)-Nets in Base 4

Best Known (79, 79+167, s)-Nets in Base 4

(79, 79+167, 104)-Net over F₄ — Constructive and digital

Digital (79, 246, 104)-net over F₄, using

t-expansion [i] based on digital (73, 246, 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]

(79, 79+167, 112)-Net over F₄ — Digital

Digital (79, 246, 112)-net over F₄, using

t-expansion [i] based on digital (73, 246, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(79, 79+167, 566)-Net in Base 4 — Upper bound on s

There is no (79, 246, 567)-net in base 4, because

1 times m-reduction [i] would yield (79, 245, 567)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3312 842622 060799 191879 896860 349472 869602 860864 194419 908996 480928 407244 230064 132944 308290 832181 318525 418058 557621 307754 227616 158517 851966 977894 526080 > 4²⁴⁵ [i]