MinT - Best Known (82, 217, s)-Nets in Base 4

Best Known (82, 217, s)-Nets in Base 4

(82, 217, 104)-Net over F₄ — Constructive and digital

Digital (82, 217, 104)-net over F₄, using

t-expansion [i] based on digital (73, 217, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(82, 217, 129)-Net over F₄ — Digital

Digital (82, 217, 129)-net over F₄, using

t-expansion [i] based on digital (81, 217, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(82, 217, 696)-Net in Base 4 — Upper bound on s

There is no (82, 217, 697)-net in base 4, because

1 times m-reduction [i] would yield (82, 216, 697)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11658 170439 462312 094141 650022 107283 446815 104929 110280 616315 744246 108593 128793 332257 007149 522892 568161 813414 344076 381155 307774 187280 > 4²¹⁶ [i]