MinT - Best Known (197−123, 197, s)-Nets in Base 4

Best Known (197−123, 197, s)-Nets in Base 4

(197−123, 197, 104)-Net over F₄ — Constructive and digital

Digital (74, 197, 104)-net over F₄, using

t-expansion [i] based on digital (73, 197, 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]

(197−123, 197, 112)-Net over F₄ — Digital

Digital (74, 197, 112)-net over F₄, using

t-expansion [i] based on digital (73, 197, 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]

(197−123, 197, 626)-Net in Base 4 — Upper bound on s

There is no (74, 197, 627)-net in base 4, because

1 times m-reduction [i] would yield (74, 196, 627)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10565 430847 279622 923465 600560 469367 102063 814507 196116 930758 592086 328254 536648 867064 624593 498237 185993 503432 023260 289312 > 4¹⁹⁶ [i]