MinT - Best Known (106, 106+128, s)-Nets in Base 4

Best Known (106, 106+128, s)-Nets in Base 4

(106, 106+128, 130)-Net over F₄ — Constructive and digital

Digital (106, 234, 130)-net over F₄, using

t-expansion [i] based on digital (105, 234, 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]

(106, 106+128, 144)-Net over F₄ — Digital

Digital (106, 234, 144)-net over F₄, using

t-expansion [i] based on digital (91, 234, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(106, 106+128, 1255)-Net in Base 4 — Upper bound on s

There is no (106, 234, 1256)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 787 024409 628930 438364 802897 563573 538486 886944 134087 166413 990377 779251 741027 771798 378243 630913 153766 215491 093586 008984 199362 102958 938500 669865 > 4²³⁴ [i]