MinT - Best Known (198−81, 198, s)-Nets in Base 4

Best Known (198−81, 198, s)-Nets in Base 4

(198−81, 198, 130)-Net over F₄ — Constructive and digital

Digital (117, 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]

(198−81, 198, 269)-Net over F₄ — Digital

Digital (117, 198, 269)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−81, 198, 4818)-Net in Base 4 — Upper bound on s

There is no (117, 198, 4819)-net in base 4, because

1 times m-reduction [i] would yield (117, 197, 4819)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 40657 079728 366755 459940 740203 965639 312924 390730 343835 224539 232534 214155 839570 954604 619579 950251 474838 455429 581467 524620 > 4¹⁹⁷ [i]