MinT - Best Known (219−103, 219, s)-Nets in Base 4

Best Known (219−103, 219, s)-Nets in Base 4

(219−103, 219, 130)-Net over F₄ — Constructive and digital

Digital (116, 219, 130)-net over F₄, using

t-expansion [i] based on digital (105, 219, 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]

(219−103, 219, 189)-Net over F₄ — Digital

Digital (116, 219, 189)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−103, 219, 2437)-Net in Base 4 — Upper bound on s

There is no (116, 219, 2438)-net in base 4, because

1 times m-reduction [i] would yield (116, 218, 2438)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 180786 286373 876814 445205 091901 377601 341522 273458 818375 665502 509429 118402 104897 193001 513361 297991 959701 369570 552455 915223 648728 207120 > 4²¹⁸ [i]