MinT - Best Known (216−100, 216, s)-Nets in Base 4

Best Known (216−100, 216, s)-Nets in Base 4

(216−100, 216, 130)-Net over F₄ — Constructive and digital

Digital (116, 216, 130)-net over F₄, using

t-expansion [i] based on digital (105, 216, 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]

(216−100, 216, 196)-Net over F₄ — Digital

Digital (116, 216, 196)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−100, 216, 2549)-Net in Base 4 — Upper bound on s

There is no (116, 216, 2550)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11109 006914 530923 450075 156690 326177 366144 704571 965353 767461 235476 855601 448018 849118 198739 613136 824546 628132 902492 442255 634676 478870 > 4²¹⁶ [i]