MinT - Best Known (79, 79+83, s)-Nets in Base 4

Best Known (79, 79+83, s)-Nets in Base 4

(79, 79+83, 104)-Net over F₄ — Constructive and digital

Digital (79, 162, 104)-net over F₄, using

t-expansion [i] based on digital (73, 162, 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+83, 112)-Net over F₄ — Digital

Digital (79, 162, 112)-net over F₄, using

t-expansion [i] based on digital (73, 162, 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+83, 1211)-Net in Base 4 — Upper bound on s

There is no (79, 162, 1212)-net in base 4, because

1 times m-reduction [i] would yield (79, 161, 1212)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 792281 949097 253963 130791 629660 942979 191454 974145 996605 572007 036205 861276 887295 056597 966767 238445 > 4¹⁶¹ [i]