MinT - Best Known (218−95, 218, s)-Nets in Base 4

Best Known (218−95, 218, s)-Nets in Base 4

(218−95, 218, 130)-Net over F₄ — Constructive and digital

Digital (123, 218, 130)-net over F₄, using

t-expansion [i] based on digital (105, 218, 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]

(218−95, 218, 239)-Net over F₄ — Digital

Digital (123, 218, 239)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−95, 218, 3648)-Net in Base 4 — Upper bound on s

There is no (123, 218, 3649)-net in base 4, because

1 times m-reduction [i] would yield (123, 217, 3649)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 44514 846794 064588 135823 120625 662856 608200 217478 845854 791141 582592 827705 322748 335306 933841 452018 896556 630805 965246 019335 614212 287040 > 4²¹⁷ [i]