MinT - Best Known (125, 125+128, s)-Nets in Base 4

Best Known (125, 125+128, s)-Nets in Base 4

(125, 125+128, 130)-Net over F₄ — Constructive and digital

Digital (125, 253, 130)-net over F₄, using

t-expansion [i] based on digital (105, 253, 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]

(125, 125+128, 176)-Net over F₄ — Digital

Digital (125, 253, 176)-net over F₄, using

net from sequence [i] based on digital (125, 175)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 125 and N(F) ≥ 176, using
  - Drinfeld modules of rank 1 [i]

(125, 125+128, 1920)-Net in Base 4 — Upper bound on s

There is no (125, 253, 1921)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 211 207970 668476 016348 237859 730298 383497 079352 769506 152059 351767 428475 997136 483064 305343 741649 163129 339800 862007 322400 689439 361306 898336 788878 141447 513130 > 4²⁵³ [i]