MinT - Best Known (218−99, 218, s)-Nets in Base 4

Best Known (218−99, 218, s)-Nets in Base 4

(218−99, 218, 130)-Net over F₄ — Constructive and digital

Digital (119, 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]

(218−99, 218, 210)-Net over F₄ — Digital

Digital (119, 218, 210)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−99, 218, 2914)-Net in Base 4 — Upper bound on s

There is no (119, 218, 2915)-net in base 4, because

1 times m-reduction [i] would yield (119, 217, 2915)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 44982 912292 484999 134418 338893 455066 502082 805962 898307 165683 550704 406276 463364 792628 932320 494535 304409 365898 327568 836066 352743 288952 > 4²¹⁷ [i]