MinT - Best Known (204−89, 204, s)-Nets in Base 4

Best Known (204−89, 204, s)-Nets in Base 4

(204−89, 204, 130)-Net over F₄ — Constructive and digital

Digital (115, 204, 130)-net over F₄, using

t-expansion [i] based on digital (105, 204, 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]

(204−89, 204, 225)-Net over F₄ — Digital

Digital (115, 204, 225)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(204−89, 204, 3411)-Net in Base 4 — Upper bound on s

There is no (115, 204, 3412)-net in base 4, because

1 times m-reduction [i] would yield (115, 203, 3412)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 166 654867 215579 515714 959829 745877 184625 776232 441757 049050 542533 537214 677719 376517 986758 416453 863249 415376 728146 785521 915160 > 4²⁰³ [i]