MinT - Best Known (218−111, 218, s)-Nets in Base 4

Best Known (218−111, 218, s)-Nets in Base 4

(218−111, 218, 130)-Net over F₄ — Constructive and digital

Digital (107, 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]

(218−111, 218, 147)-Net over F₄ — Digital

Digital (107, 218, 147)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−111, 218, 1643)-Net in Base 4 — Upper bound on s

There is no (107, 218, 1644)-net in base 4, because

1 times m-reduction [i] would yield (107, 217, 1644)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 45273 617378 884912 285133 087262 596354 325232 585909 078889 011131 209397 786882 174452 066587 413910 438466 130229 964849 395980 498297 917516 884168 > 4²¹⁷ [i]