MinT - Best Known (198−80, 198, s)-Nets in Base 4

Best Known (198−80, 198, s)-Nets in Base 4

(198−80, 198, 130)-Net over F₄ — Constructive and digital

Digital (118, 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]

(198−80, 198, 280)-Net over F₄ — Digital

Digital (118, 198, 280)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−80, 198, 4989)-Net in Base 4 — Upper bound on s

There is no (118, 198, 4990)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 162507 062640 511417 992240 700744 452238 901682 545664 677978 122801 620015 382664 373467 531694 794962 661369 978952 080844 715708 710985 > 4¹⁹⁸ [i]