MinT - Best Known (111, 198, s)-Nets in Base 4

Best Known (111, 198, s)-Nets in Base 4

(111, 198, 130)-Net over F₄ — Constructive and digital

Digital (111, 198, 130)-net over F₄, using

t-expansion [i] based on digital (105, 198, 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]

(111, 198, 214)-Net over F₄ — Digital

Digital (111, 198, 214)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 198, 3190)-Net in Base 4 — Upper bound on s

There is no (111, 198, 3191)-net in base 4, because

1 times m-reduction [i] would yield (111, 197, 3191)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 40617 315092 074536 605636 273301 786747 878255 510929 696442 525032 915254 229199 998030 003864 044858 692239 616563 507580 118501 933520 > 4¹⁹⁷ [i]