MinT - Best Known (219−101, 219, s)-Nets in Base 4

Best Known (219−101, 219, s)-Nets in Base 4

(219−101, 219, 130)-Net over F₄ — Constructive and digital

Digital (118, 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]

(219−101, 219, 201)-Net over F₄ — Digital

Digital (118, 219, 201)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−101, 219, 2697)-Net in Base 4 — Upper bound on s

There is no (118, 219, 2698)-net in base 4, because

1 times m-reduction [i] would yield (118, 218, 2698)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 178668 753398 537682 663427 041703 795274 595236 174515 041895 389629 195579 113607 038236 330589 863027 410768 261696 027793 200866 265616 007005 711328 > 4²¹⁸ [i]