MinT - Best Known (79, 79+169, s)-Nets in Base 4

Best Known (79, 79+169, s)-Nets in Base 4

(79, 79+169, 104)-Net over F₄ — Constructive and digital

Digital (79, 248, 104)-net over F₄, using

t-expansion [i] based on digital (73, 248, 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]

(79, 79+169, 112)-Net over F₄ — Digital

Digital (79, 248, 112)-net over F₄, using

t-expansion [i] based on digital (73, 248, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(79, 79+169, 563)-Net in Base 4 — Upper bound on s

There is no (79, 248, 564)-net in base 4, because

1 times m-reduction [i] would yield (79, 247, 564)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 55606 013443 761918 974159 014373 621556 196206 094166 927606 842502 786284 484117 851166 191155 354914 888228 374901 563287 531869 449573 081864 259113 276436 561889 292480 > 4²⁴⁷ [i]