MinT - Best Known (102, 102+144, s)-Nets in Base 4

Best Known (102, 102+144, s)-Nets in Base 4

(102, 102+144, 104)-Net over F₄ — Constructive and digital

Digital (102, 246, 104)-net over F₄, using

t-expansion [i] based on digital (73, 246, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(102, 102+144, 144)-Net over F₄ — Digital

Digital (102, 246, 144)-net over F₄, using

t-expansion [i] based on digital (91, 246, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(102, 102+144, 992)-Net in Base 4 — Upper bound on s

There is no (102, 246, 993)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13446 912983 530374 753856 929597 039680 944765 480711 387109 045873 468379 241061 243005 253700 502068 364636 759975 197808 871561 511168 541615 229696 947601 014474 142332 > 4²⁴⁶ [i]