MinT - Best Known (118, 118+109, s)-Nets in Base 4

Best Known (118, 118+109, s)-Nets in Base 4

(118, 118+109, 130)-Net over F₄ — Constructive and digital

Digital (118, 227, 130)-net over F₄, using

t-expansion [i] based on digital (105, 227, 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]

(118, 118+109, 183)-Net over F₄ — Digital

Digital (118, 227, 183)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(118, 118+109, 2268)-Net in Base 4 — Upper bound on s

There is no (118, 227, 2269)-net in base 4, because

1 times m-reduction [i] would yield (118, 226, 2269)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11708 398452 351997 402755 133441 091606 630967 236074 654260 039205 178852 950179 984295 612239 716956 493139 620779 548439 927273 977340 910223 327523 893304 > 4²²⁶ [i]