MinT - Best Known (197−77, 197, s)-Nets in Base 4

Best Known (197−77, 197, s)-Nets in Base 4

(197−77, 197, 130)-Net over F₄ — Constructive and digital

Digital (120, 197, 130)-net over F₄, using

t-expansion [i] based on digital (105, 197, 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]

(197−77, 197, 311)-Net over F₄ — Digital

Digital (120, 197, 311)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−77, 197, 6352)-Net in Base 4 — Upper bound on s

There is no (120, 197, 6353)-net in base 4, because

1 times m-reduction [i] would yield (120, 196, 6353)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10136 708638 494250 263136 506201 537795 539612 699276 665077 790923 925779 318124 294408 405105 994451 543787 656954 754181 170718 834320 > 4¹⁹⁶ [i]