MinT - Best Known (198−85, 198, s)-Nets in Base 4

Best Known (198−85, 198, s)-Nets in Base 4

(198−85, 198, 130)-Net over F₄ — Constructive and digital

Digital (113, 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]

(198−85, 198, 231)-Net over F₄ — Digital

Digital (113, 198, 231)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−85, 198, 3635)-Net in Base 4 — Upper bound on s

There is no (113, 198, 3636)-net in base 4, because

1 times m-reduction [i] would yield (113, 197, 3636)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 40668 636418 037592 898488 649385 594083 534872 120508 874981 876260 694486 409786 471442 292534 507640 258921 962639 223318 177534 029470 > 4¹⁹⁷ [i]