MinT - Best Known (260−150, 260, s)-Nets in Base 4

Best Known (260−150, 260, s)-Nets in Base 4

(260−150, 260, 130)-Net over F₄ — Constructive and digital

Digital (110, 260, 130)-net over F₄, using

t-expansion [i] based on digital (105, 260, 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]

(260−150, 260, 165)-Net over F₄ — Digital

Digital (110, 260, 165)-net over F₄, using

t-expansion [i] based on digital (109, 260, 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]

(260−150, 260, 1110)-Net in Base 4 — Upper bound on s

There is no (110, 260, 1111)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 572714 704446 085540 314179 111382 376111 270307 044115 700553 680042 702221 427175 290296 554740 378661 931311 044238 701682 173052 355594 599735 383018 275758 792968 265451 781136 > 4²⁶⁰ [i]