MinT - Best Known (110, 110+128, s)-Nets in Base 4

Best Known (110, 110+128, s)-Nets in Base 4

(110, 110+128, 130)-Net over F₄ — Constructive and digital

Digital (110, 238, 130)-net over F₄, using

t-expansion [i] based on digital (105, 238, 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]

(110, 110+128, 165)-Net over F₄ — Digital

Digital (110, 238, 165)-net over F₄, using

t-expansion [i] based on digital (109, 238, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(110, 110+128, 1373)-Net in Base 4 — Upper bound on s

There is no (110, 238, 1374)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 198583 508580 318276 773134 090632 037412 978824 183635 207447 135970 973934 316570 282098 507879 627104 467969 021486 371129 430935 514708 263157 475715 571481 903569 > 4²³⁸ [i]