MinT - Best Known (109, 109+83, s)-Nets in Base 4

Best Known (109, 109+83, s)-Nets in Base 4

(109, 109+83, 130)-Net over F₄ — Constructive and digital

Digital (109, 192, 130)-net over F₄, using

t-expansion [i] based on digital (105, 192, 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]

(109, 109+83, 220)-Net over F₄ — Digital

Digital (109, 192, 220)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+83, 3398)-Net in Base 4 — Upper bound on s

There is no (109, 192, 3399)-net in base 4, because

1 times m-reduction [i] would yield (109, 191, 3399)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 949158 822115 676318 658194 188090 007738 674888 704708 144444 944387 297795 047718 982893 176801 797999 142129 062072 978010 831312 > 4¹⁹¹ [i]