MinT - Best Known (244−124, 244, s)-Nets in Base 4

Best Known (244−124, 244, s)-Nets in Base 4

(244−124, 244, 130)-Net over F₄ — Constructive and digital

Digital (120, 244, 130)-net over F₄, using

t-expansion [i] based on digital (105, 244, 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]

(244−124, 244, 168)-Net over F₄ — Digital

Digital (120, 244, 168)-net over F₄, using

t-expansion [i] based on digital (115, 244, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(244−124, 244, 1816)-Net in Base 4 — Upper bound on s

There is no (120, 244, 1817)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 801 271618 536984 891073 525616 419959 504206 039818 787297 313560 039294 247069 716447 199564 286753 036069 227645 327716 356830 927712 251904 957418 434390 151495 128960 > 4²⁴⁴ [i]